x=4/2x-5=3/5

Solution for x=4/2x-5=3/5 equation:

x=4/2x-5=3/5

We move all terms to the left:

x-(4/2x-5)=0


Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

x-4/2x+5=0

We multiply all the terms by the denominator


x*2x+5*2x-4=0

Wy multiply elements

2x^2+10x-4=0

a = 2; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·2·(-4)
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*2}=\frac{-10-2\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*2}=\frac{-10+2\sqrt{33}}{4}
$